The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  0  0  0  X  X  0  0  X  1  1  0  1  X  1  X
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  1  1  0  X  1  1  0  0  X  0  X X+1  1  0  X
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  0  X  1  1  1 X+1  1  1  X  1  1  X  0  X  1
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  0  0  X  0  0  X  X  X  0  X  X  0
 0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  0  0  X  0  X  X  0  X  0  X  0  0  X
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  0  X  0  X  0  X  X  0  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  X  0  X  X  0  0  X
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  X  X  0  X  X  X  X  0  X  X  X  0  X

generates a code of length 29 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+81x^22+56x^23+122x^24+160x^25+152x^26+184x^27+144x^28+224x^29+179x^30+200x^31+175x^32+128x^33+84x^34+72x^35+64x^36+11x^38+6x^40+4x^42+1x^46

The gray image is a linear code over GF(2) with n=58, k=11 and d=22.
This code was found by Heurico 1.16 in 0.282 seconds.